Jan W. Cholewa, Silesian University, 40-007 Katowice, Poland, e-mail: jan.cholewa@us.edu.pl; Anibal Rodriguez-Bernal, Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain and Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, e-mail: arober@mat.ucm.es
Abstract: We consider the Cahn-Hilliard equation in $H^1(\mathbb R^N)$ with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as $|u|\to\infty$ and logistic type nonlinearities. In both situations we prove the $H^2(\mathbb R^N)$-bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).
Keywords: initial value problem for higher order parabolic equations; asymptotic behavior of solutions; critical exponent
Classification (MSC 2010): 35K30, 35B40, 35B33
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